Part of Encyclopedia of Mathematics and its Applications
Publication planned for: December 2018
availability: Not yet published - available from December 2018
format: Hardback
isbn: 9781108470599
Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 …, and the natural logarithm base, e = 2.178 …. Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson?Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl?Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton-Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
1. Number theory and combinatorics
2. Inequalities and approximation
3. Real and complex analysis
4. Probability and stochastic processes
5. Geometry and topology
Index.
Part of Institute of Mathematical Statistics Textbooks
Publication planned for: December 2018
format: Hardback
isbn: 9781107039124
format: Paperback
isbn: 9781107611986
This textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research. It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion. The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Levy processes and stochastic calculus for jump processes. Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.
Preface
1. Brownian motion
2. Stochastic calculus
3. Derivative and divergence operators
4. Wiener chaos
5. Ornstein-Uhlenbeck semigroup
6. Stochastic integral representations
7. Study of densities
8. Normal approximations
9. Jump processes
10. Malliavin calculus for jump processes I
11. Malliavin calculus for jump processes II
Appendix A. Basics of stochastic processes
References
Index.
Part of London Mathematical Society Lecture Note Series
available from December 2018
format: Paperback
isbn: 9781108460965
The Euler and Navier?Stokes equations are the fundamental mathematical models of fluid mechanics, and their study has greatly informed our understanding of the behaviour of complex fluids. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains surveys of recent progress and classical topics, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models, and several chapters address the Navier?Stokes equations directly, in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researchers.
Preface Charles L. Fefferman, James C. Robinson and Jose L. Rodrigo
1. Remarks on recent advances concerning boundary effects and the vanishing viscosity limit of the Navier?Stokes equations Claude Bardos
2. Time-periodic flow of a viscous liquid past a body Giovanni P. Galdi and Mads Kyed
3. The Rayleigh?Taylor instability in buoyancy-driven variable density turbulence John D. Gibbon, Pooja Rao and Colm-Cille P. Caulfield
4. On localization and quantitative uniqueness for elliptic partial differential equations Guher Camliyurt, Igor Kukavica and Fei Wang
5. Quasi-invariance for the Navier?Stokes equations Koji Ohkitani
6. Leray's fundamental work on the Navier?Stokes equations: a modern review of 'Sur le mouvement d'un liquide visqueux emplissant l'espace' Wojciech S. O?a?ski and Benjamin C. Pooley
7. Stable mild Navier?Stokes solutions by iteration of linear singular Volterra integral equations Reimund Rautmann
8. Energy conservation in the 3D Euler equations on T2 x R+ James C. Robinson, Jose L. Rodrigo and Jack W. D. Skipper
9. Regularity of Navier?Stokes flows with bounds for the velocity gradient along streamlines and an effective pressure Chuong V. Tran and Xinwei Yu
10. A direct approach to Gevrey regularity on the half-space Igor Kukavica and Vlad Vicol
11. Weak-strong uniqueness in fluid dynamics Emil Wiedemann.
Part of Cambridge Studies in Advanced Mathematics
available from December 2018
format: Hardback
isbn: 9781108428033
This text organizes a range of results in chromatic homotopy theory, running a single thread through theorems in bordism and a detailed understanding of the moduli of formal groups. It emphasizes the naturally occurring algebro-geometric models that presage the topological results, taking the reader through a pedagogical development of the field. In addition to forming the backbone of the stable homotopy category, these ideas have found application in other fields: the daughter subject 'elliptic cohomology' abuts mathematical physics, manifold geometry, topological analysis, and the representation theory of loop groups. The common language employed when discussing these subjects showcases their unity and guides the reader breezily from one domain to the next, ultimately culminating in the construction of Witten's genus for String manifolds. This text is an expansion of a set of lecture notes for a topics course delivered at Harvard University during the spring term of 2016.
Foreword Matthew Ando
Preface
Introduction
1. Unoriented bordism
2. Complex bordism
3. Finite spectra
4. Unstable cooperations
5. The σ-orientation
Appendix A. Power operations
Appendix B. Loose ends
References
Index.